Signals and Systems - Fourier Transform

Consider a continuous-time, real-valued signal f(t) whose Fourier transform F(ω) = ∫_(-∞)^∞ f(t) exp(-j ωt) dt exists. Which one of the following statements is always TRUE?

Consider two continuous time signals $x(t)$ and $y(t)$ as shown below If $X(f)$ denotes the Fourier transform of $x(t)$, then the Fourier transform of $y(t)$ is ________.

The Fourier transform X(ω) of x(t) = e⁻ᵗ² is Note: ∫₋∞^∞ e⁻ʸ² dy = √π